Straight lines `y=m x+c_1` and `y=m x+c_2` where `m in R^+,` meet the x-axis at `A_1a n dA_2,` respectively, and the y-axis at `B_1a n dB_2,` respectively. It is given that points `A_1,A_2,B_1,` and `B_2` are concylic. Find the locus of the intersection of lines `A_1B_2` and `A_2B_1` .

The line x/a+y/b=1 meets the axis of and y at A and B respectively and C is middle point of AB then

If the tangent and the normal to x^2-y^2=4 at a point cut off intercepts a_1,a_2 on the x-axis respectively & b_1,b_2 on the y-axis respectively. Then the value of a_1a_2+b_1b_2 is equal to:

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

A straight line through the point (1,1) meets the X-axis at A and Y-axis at B. The locus of the mid-point of AB is

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot

If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db ,c respectively, then prove that a/x+c/y=2a n d1/x+1/y=2/b

A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to the parabola at Aa n dB meet the y-axis at A_1a n dB_1 , respectively. If the area of trapezium AA_1B_1B is equal to 12 a^2, then the angle subtended by A_1B_1 at the focus of the parabola is equal to 2tan^(-1)(3) (b) tan^(-1)(3) 2tan^(-1)(2) (d) tan^(-1)(2)

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a xdot Prove m_1m_2=-1.